Problem
Research questions and friction points this paper is trying to address.
causal discovery
statistical inference
functional causal model
hypothesis testing
goodness-of-fit
Statistical Inference for Bivariate Functional Causal Discovery
๐ค AI Summary
ๆฌๆ้ๅฏนๅ่ฝๅ ๆๅ็ฐๆนๆณ็ผบไน็ป่ฎกๆจๆญ็้ฎ้ข๏ผๆๅบไบไธ็งๅบไบๅ่ฎพๆฃ้ช็ๆนๆณ๏ผๅฉ็จๆๅไผๅบฆๅ็ฌ็ซๆงๆต่ฏๆฅ็กฎๅฎๅๅ้้ด็ๅ ๆๆนๅใ
๐ Abstract
Causal discovery methods aim to determine the causal direction between variables using observational data. Functional causal discovery methods rely on structural and distributional assumptions to determine directionality but typically lack statistical inference. This paper reviews the statistical guarantees of existing functional causal discovery methods in theory, software, and applied use, highlighting a key gap: the absence of a unified inferential framework that applies broadly across model classes. As a first step toward addressing this gap, we formalize a test-based approach for bivariate causal discovery by repurposing goodness-of-fit and independence tests within a hypothesis-testing framework. Because directionality is determined through two disjoint hypothesis tests, corresponding to four causal discovery outcomes, the approach provides explicit uncertainty quantification and diagnostic insight into assumption violations. Resampling is further used to estimate the rates of causal discovery outcomes, offering an additional layer of inference. We demonstrate the use and behavior of our inferential framework through simulations that vary the degree of assumption violation, as well as through real-data applications. We conclude with practical lessons and recommendations for advancing statistical guarantees in functional causal discovery.
Innovation
Methods, ideas, or system contributions that make the work stand out.
test-based approach
uncertainty quantification
resampling
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